Question: Define $a \Delta b = a^2 -b $.  What is the value of $ (2^{4 \Delta13})\Delta(3^{3\Delta5})$
Solution: We have $4 \Delta 13 = 4^2-13=16-13=3$ and $3 \Delta 5 = 3^2-5 = 9-5=4$. Thus we are looking for $(2^3) \Delta (3^4) = 2^6-3^4 = 64-81 = \boxed{-17}$.